The area enclosed by the curves y = x^ 3 and y = x is

Since, the intersection of two curves

$y = x^{3}$ and $y = \sqrt{x}$ are $x = 0$ and $x = 1$

$∴ A = \left|{∫}_{0}^{1}\left(x^{3} - \sqrt{x}\right)dx\right| = \left|{\dfrac{x4}{4} - \dfrac{2x^{3 / 2}}{3}}_{0}^{1}\right|$

$= \left|\left[\dfrac{1}{4} - \dfrac{2}{3}\right]\right| = \dfrac{5}{12}squnits$